Horizons as boundary conditions in spherical symmetry

Understand

We initiate the development of a horizon-based initial (or rather final) value formalism to describe the geometry and physics of the near-horizon spacetime: data specified on the horizon and a future ingoing null boundary determine the near-horizon geometry.

• In this initial paper we restrict our attention to spherically symmetric spacetimes made dynamic by matter fields.
• We illustrate the formalism by considering a black hole interacting with a) inward-falling, null matter (with no outward flux) and b) a massless scalar field.
• The inward-falling case can be exactly solved from horizon data.